Let
![P(z)](/media/m/4/c/c/4ccb0cbb349a868004cc5e2c28314c79.png)
and
![Q(z)](/media/m/8/f/0/8f02c780957fc0ce56c5434727fc63e3.png)
be complex-variable polynomials, with degree not less than
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
. Let
![P_k = \{z \in \mathbb C | P(z) = k \}, Q_k = \{ z \in \mathbb C | Q(z) = k \}.](/media/m/1/7/b/17b48c6c682bf796288e4ad305dff156.png)
Let also
![P_0 = Q_0](/media/m/8/7/b/87b27cbbd271bdc672b8f0ef89a9332e.png)
and
![P_1 = Q_1](/media/m/f/1/9/f1940845b493fc0f3723975981a78f89.png)
. Prove that
%V0
Let $P(z)$ and $Q(z)$ be complex-variable polynomials, with degree not less than $1$. Let
$$P_k = \{z \in \mathbb C | P(z) = k \}, Q_k = \{ z \in \mathbb C | Q(z) = k \}.$$
Let also $P_0 = Q_0$ and $P_1 = Q_1$. Prove that $P(z) \equiv Q(z).$